Sometimes good advice fails and you need a dramatic example. So here’s mine.
One of Raoul’s observations on life has played a crucial role in my mental equilibrium. When he was at the Institute for Advanced Study at Princeton in 1949-51, he once had a conversation with John von Neumann, a fellow Hungarian who was at the time a professor at the institute. Von Neumann told Raoul that he had known only one great mathematician, David Hilbert, and that having been a prodigy in his youth, he never felt that he had lived up to his promise. Raoul wrote, “So you see, it is not difficult to be found wanting—one just needs an appropriate measuring rod.” If even von Neumann felt inadequate in his achievement in comparison with Hilbert’s, what chance for professional satisfaction do we ordinary mortals have? After Raoul recounted this incident to me, I resolved never to compare myself with anyone else, especially not with my friends and classmates who have achieved greatness.
Perhaps the only mathematician who never envied anyone was Euclid. But I think he’d kill for the truths found in the 2000 years since.